docs: def getFreeEnergyDifferences(self, compute_uncertainty=True, uncertainty_method=None, warning_cutoff=1.0e-10, return_theta=False):
          """Get the dimensionless free energy differences and uncertainties among all thermodynamic states.
  
  
          Parameters
          ----------
          compute_uncertainty : bool, optional
              If False, the uncertainties will not be computed (default: True)
          uncertainty_method : string, optional
              Choice of method used to compute asymptotic covariance method,
              or None to use default.  See help for computeAsymptoticCovarianceMatrix()
              for more information on various methods. (default: svd)
          warning_cutoff : float, optional
              Warn if squared-uncertainty is negative and larger in magnitude
              than this number (default: 1.0e-10)
          return_theta : bool, optional
              Whether or not to return the theta matrix.  Can be useful for complicated differences.
  
          Returns
          -------
          result_vals : dictionary
  
          Possible keys in the result_vals dictionary:
  
          'Delta_f' : np.ndarray, float, shape=(K, K)
              Deltaf_ij[i,j] is the estimated free energy difference
          'dDelta_f' : np.ndarray, float, shape=(K, K)
              If compute_uncertainty==True,
              dDeltaf_ij[i,j] is the estimated statistical uncertainty
              (one standard deviation) in Deltaf_ij[i,j].  Otherwise not included.
          'Theta' : np.ndarray, float, shape=(K, K)
              The theta_matrix if return_theta==True, otherwise not included.
  
          Notes
          -----
          Computation of the covariance matrix may take some time for large K.
  
          The reported statistical uncertainty should, in the asymptotic limit, reflect one standard deviation for the normal distribution of the estimate.
          The true free energy difference should fall within the interval [-df, +df] centered on the estimate 68% of the time, and within
          the interval [-2 df, +2 df] centered on the estimate 95% of the time.
          This will break down in cases where the number of samples is not large enough to reach the asymptotic normal limit.
  
          See Section III of Reference [1].
  
          Examples
          --------
  
          >>> from pymbar import testsystems
          >>> (x_n, u_kn, N_k, s_n) = testsystems.HarmonicOscillatorsTestCase().sample(mode='u_kn')
          >>> mbar = MBAR(u_kn, N_k)
          >>> results = mbar.getFreeEnergyDifferences()
  
          """
          Deltaf_ij, dDeltaf_ij, Theta_ij = None, None, None  # By default, returns None for dDelta and Theta
  
          # Compute free energy differences.
          f_i = np.matrix(self.f_k)
          Deltaf_ij = f_i - f_i.transpose()
  
          # zero out numerical error for thermodynamically identical states
          self._zerosamestates(Deltaf_ij)
  
          Deltaf_ij = np.array(Deltaf_ij)  # Convert from np.matrix to np.array
  
          result_vals = dict()
  
          result_vals['Delta_f'] = Deltaf_ij
  
          if compute_uncertainty or return_theta:
              # Compute asymptotic covariance matrix.
              Theta_ij = self._computeAsymptoticCovarianceMatrix(
                  np.exp(self.Log_W_nk), self.N_k, method=uncertainty_method)
  
          if compute_uncertainty:
              dDeltaf_ij = self._ErrorOfDifferences(Theta_ij, warning_cutoff=warning_cutoff)
              # zero out numerical error for thermodynamically identical states
              self._zerosamestates(dDeltaf_ij)
              # Return matrix of free energy differences and uncertainties.
              dDeltaf_ij = np.array(dDeltaf_ij)
              result_vals['dDelta_f'] = dDeltaf_ij
  
          if return_theta:
              result_vals['Theta'] = Theta_ij
  
          return result_vals